Course name: Foundations of Financial Management (10248) – Fall I, 2013

Assignment name: Week 6 Questions/Problems

Problem 7-9

Declining Growth Stock Valuation

1. Brushy Mountain Mining Company’s ore reserves are being depleted, so its sales are falling. Also, its pit is getting deeper each year, so its costs are rising. As a result, the company’s earnings and dividends are declining at the constant rate of 4% per year. If D0 = $6 and rs = 18%, what is the value of Brushy Mountain Mining’s stock? Round your answer to the nearest cent.

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Problem 7-4

Preferred Stock Valuation

2. Nick’s Enchiladas Incorporated has preferred stock outstanding that pays a dividend of $3 at the end of each year. The preferred stock sells for $40 a share. What is the stock’s required rate of return? Round the answer to two decimal places.

Problem 7-2

Constant Growth Valuation

Boehm Incorporated is expected to pay a $3.40 per share dividend at the end of this year (i.e., D1 = $3.40). The dividend is expected to grow at a constant rate of 10% a year. The required rate of return on the stock, rs, is 17%. What is the value per share of the company’s stock? Round your answer to the nearest cent.

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Which of the following statements is CORRECT?

a. The constant growth model takes into consideration the capital gains investors expect to earn on a stock.

b. Two firms with the same expected dividend and growth rates must also have the same stock price.

c. It is appropriate to use the constant growth model to estimate a stock’s value even if its growth rate is never expected to become constant.

d. If a stock has a required rate of return rs = 12%, and if its dividend is expected to grow at a constant rate of 5%, this implies that the stock’s dividend yield is also 5%.

e. The price of a stock is the present value of all expected future dividends, discounted at the dividend growth rate.

If in the opinion of a given investor a stock’s expected return exceeds its required return, this suggests that the investor thinks

a. the stock should be sold.

b. the stock is a good buy.

c. management is probably not trying to maximize the price per share.

d. dividends are not likely to be declared.

e. the stock is experiencing supernormal growth.

Companies can issue different classes of common stock. Which of the following statements concerning stock classes is CORRECT?

a. All firms have several classes of common stock.

b. All common stocks, regardless of class, must have the same voting rights.

c. All common stocks fall into one of three classes: A, B, and C.

d. Some class or classes of common stock are entitled to more votes per share than other classes.

e. All common stock, regardless of class, must pay the same dividend.

7.Which of the following statements is CORRECT, assuming stocks are in equilibrium?

a. Assume that the required return on a given stock is 13%. If the stock’s dividend is growing at a constant rate of 5%, its expected dividend yield is 5% as well.

b. A required condition for one to use the constant growth model is that the stock’s expected growth rate exceeds its required rate of return.

c. The dividend yield on a constant growth stock must equal its expected total return minus its expected capital gains yield.

d. A stock’s dividend yield can never exceed its expected growth rate.

e. Other things held constant, the higher a company’s beta coefficient, the lower its required rate of return.

8. A share of common stock just paid a dividend of $1.00. If the expected long-run growth rate for this stock is 5.4%, and if investors’ required rate of return is 11.4%, what is the stock price?

a. $17.13

b. $16.70

c. $17.57

d. $16.28

e. $18.01

9. A company currently pays a dividend of $3.25 per share, D0 = 3.25. It is estimated that the company’s dividend will grow at a rate of 23% percent per year for the next 2 years, then the dividend will grow at a constant rate of 6% thereafter. The company’s stock has a beta equal to 1.55, the risk-free rate is 7.5 percent, and the market risk premium is 6 percent. What is your estimate is the stock’s current price? Round your answer to the nearest cent.

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10. A stock is expected to pay a year-end dividend of $2.00, i.e., D1 = $2.00. The dividend is expected to decline at a rate of 5% a year forever (g = 5%). If the company is in equilibrium and its expected and required rate of return is 15%, which of the following statements is CORRECT?

a. The company’s current stock price is $20.

b. The company’s dividend yield 5 years from now is expected to be 10%.

c. The company’s expected capital gains yield is 5%.

d. The constant growth model cannot be used because the growth rate is negative.

e. The company’s expected stock price at the beginning of next year is $9.50.

11. The beta coefficient for Stock C is bC = 0.6, and that for Stock D is bD = – 0.6. (Stock D’s beta is negative, indicating that its rate of return rises whenever returns on most other stocks fall. There are very few negative-beta stocks, although collection agency and gold mining stocks are sometimes cited as examples.)

a. If the risk-free rate is 8%and the expected rate of return on an average stock is 11%, what are the required rates of return on Stocks C and D? Round the answers to two decimal places.

1. rC =

2. rD =

b. For Stock C, suppose the current price, P0, is $25; the next expected dividend, D1, is $1.50; and the stock’s expected constant growth rate is 4%. Is the stock in equilibrium? Explain, and describe what would happen if the stock is not in equilibrium.

I. In this situation, the expected rate of return = 9.80%. However, the required rate of return is 10%. Investors will seek to buy the stock, raising its price to $25.86. At this price, the stock will be in equilibrium.

II. In this situation, the expected rate of return = 10%. However, the required rate of return is 9.80%. Investors will seek to sell the stock, raising its price to $25.86. At this price, the stock will be in equilibrium.

III. In this situation, the expected rate of return = 9.80%. However, the required rate of return is 10%. Investors will seek to sell the stock, raising its price to $25.86. At this price, the stock will be in equilibrium.

IV. In this situation, the expected rate of return = 10%. However, the required rate of return is 9.80%. Investors will seek to buy the stock, raising its price to $25.86. At this price, the stock will be in equilibrium.

V. In this situation, both the expected rate of return and the required rate of return are equal. Therefore, the stock is in equilibrium at its current price.

12. For a stock to be in equilibrium, that is, for there to be no long-term pressure for its price to depart from its current level, then

a. the past realized return must be equal to the expected return during the same period.

b. the expected return must be equal to both the required future return and the past realized return.

c. the expected future return must be less than the most recent past realized return.

d. the expected future returns must be equal to the required return.

e. the required return must equal the realized return in all periods.

13. Investors require a 15% rate of return on Brooks Sisters’ stock (rs = 15%).

a. What would the value of Brooks’s stock be if the previous dividend was D0 = $3.25 and if investors expect dividends to grow at a constant compound annual rate of (1) – 2%, (2) 0%, (3) 7%, or (4) 12%? Round your answers to the nearest cent.

1. $

2. $

3. $

4. $

b. Using data from part a, what is the Gordon (constant growth) model’s value for Brooks Sisters’s stock if the required rate of return is 15% and the expected growth rate is (1) 15% or (2) 23%? Are these reasonable results? Explain.

1.

2.

c. Is it reasonable to expect that a constant growth stock would have g > rs?

14. The risk-free rate of return, rRF , is 11%; the required rate of return on the market, rM, 15%; and Schuler Company’s stock has a beta coefficient of 1.7.

a. If the dividend expected during the coming year, D1, is $2.00, and if g is a constant 1.75%, then at what price should Schuler’s stock sell? Round your answer to the nearest cent.

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b. Now, suppose the Federal Reserve Board increases the money supply, causing a fall in the risk-free rate to 6% and rM to 13%. How would this affect the price of the stock? Round your answer to the nearest cent.

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c. In addition to the change in part b, suppose investors’ risk aversion declines; this fact, combined with the decline in rRF, causes rM to fall to 8%. At what price would Schuler’s stock sell? Round your answer to the nearest cent.

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d. Suppose Schuler has a change in management. The new group institutes policies that increase the expected constant growth rate to 7%. Also, the new management stabilizes sales and profits, and thus causes the beta coefficient to decline from 1.7 to 0.7. Assume that rRF and rM are equal to the values in part c. After all these changes, what is Schuler’s new equilibrium price? (Note: D1 goes to $2.10.) Round your answer to the nearest cent.

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15. The expected return on Natter Corporation’s stock is 14%. The stock’s dividend is expected to grow at a constant rate of 8%, and it currently sells for $50 a share. Which of the following statements is CORRECT?

a. The stock’s dividend yield is 7%.

b. The stock’s dividend yield is 8%.

c. The current dividend per share is $4.00.

d. The stock price is expected to be $54 a share one year from now.

e. The stock price is expected to be $57 a share one year from now.